Which has more atoms: 1 kg of i ykf1aw+ r7c t2pwk:21bc da3uron or 1 kg of aluminum? See the periodic table or Apw :w3ry7aa2u+ k1dcktf12p bcpendix B.

Name several properties of materials that could be k (:ondio5zc- exploited to make a thermometerozdn:(5k-ico .

Which is larger, 1 C qf5,v,zf6oz u$^{\circ} $ or 1 F $^{\circ} $?

If system A is in thermal equilibrium with sy(4jj.o3 clh:amxk)tn stem B, but B is not in thermal equilibrium with system C, what can you say about the temperatures of A, B, and C atn:jkco( )3lh4xm.j?

A flat bimetallic strip consists of aluminum riveted to a strip98b-(x:u xz1c vhpskg of iron. When heated, ths:1xxkvg9(h8c -ub pze strip will bend. Which metal will be on the outside of the curve? [Hint: See Table 13–1.] Why?

In the relation $\Delta$L = $\alpha$ $L_0$ $\Delta$T, should $L_0$ be the initial length, the final length, or does it matter? Explain.

The units for the coefficient ,0f tya4 i wfyu m)g.ih3,wg)fof linear expansion $\alpha$ are $(C?)^{-1}$ and there is no mention of a length unit such as meters. Would the expansion coefficient change if we used feet or millimeters instead of meters? Explain.

Figure 13–27 shows a diagram of a simple thermostat77x,+;(gpteu d-dh io9cyq ip used to control a furnace (or other heating or cooling system). The bimetallic strip consists of two strips of different metals bonded together. The electric switch is a glass vessel containing gx itophdd ,q;97 ipuyc-7(e+ liquid mercury that conducts electricity when it can flow to touch both contact wires. Explain how this device controls the furnace and how it can be set at different temperatures.

Long steam pipes that are fixed at the ends often ha*,3bwfq bo w5tve a section in the shape of a U.,bo3q w*5fwtb Why?

A flat, uniform cylinder s;g97vh9cv0whbfzg kzx 29w-vbu 5splf / 5h6 of lead floats in mercury at 0 $^{\circ} $ C. Will the lead float higher or lower when the temperature is raised? Explain.

When a cold mercury-in-glass thermometer is first l9q sxq(9 bml5placed in a hot tub of water, the mercury(ll bs959 mqqx initially descends a bit and then rises. Explain.

A glass container may break if one part of it is heated or coolerzt60-ps c 9m f)hvpg68sr/ qwc95a qwd more rapidly than adjacent part 698 p0)rzt6 w5/ vmgapfcw9qsscrq-hs. Explain.

The principal virtue ozx xk rm(v0tp 9n3ks2xs3h;g/f Pyrex glass is that its coefficient of linear expansion is much smaller than that for ordinary gl 0x/xs(;xgkv3t n2hmk rp9s3zass (Table 13–1). Explain why this gives rise to the increased heat resistance of Pyrex.

Will a grandfather clock, accuratwom+l4 (/o4y8 ky0dn xm/w25b hvhmzce at 20 $^{\circ} $ C, run fast or slow on a hot day (30 $^{\circ} $ C)? Explain. The clock uses a pendulum supported on a long, thin brass rod.

Freezing a can of sodf,1re:q (x npba will cause its bottom and top to bulge so badly the can will not sneq(,pr1 xf:b tand up. What has happened?

When a gas is rapidly compressed zt2a2 k/ ku.z)hri5a m(say, by pushing down a piston), its temperature increases. When a gas expands against a piston, it cools. Explain these changes in temperature using the kinetic theory, in particular notinziah.5/z2 rmutak)k 2 g what happens to the momentum of molecules when they strike the moving piston.

Will the buoyant force on an aluminuhj(5rwqc me/ u+9dd x3m sphere submerged in water increase or decrease if(3e rmd95/ch ju +wqxd the temperature is increased from 20 $^{\circ} $ C to 40 $^{\circ} $ C?

Explain in words how Charles’s law follonrqlryw;d q/) :: f4muws from kinetic theory and the relation between average kinetic energy and the yl4r: q/ud;m)n:r w qfabsolute temperature.

Explain in words how Gay-Lussac’s law follows fro-jw.14 d8p0ixy qxsjgm kinetic theory.

As you go higher in then9lrkml p (+lotg/+;p Earth’s atmosphere, the ratio of $N_2$ molecules to $O_2$ molecules increases. Why?

Escape velocity for the Earth refers to t j5 7e605v pypxwh7qcujf1)lfhe minimum speed an object must have to leave thvjc pq7w f7jl 0y) uhxf1p55e6e Earth and never return. The escape velocity for the Moon is about one-fifth what it is for the Earth due to the Moon’s smaller mass. Explain why the Moon has practically no atmosphere.

Alcohol evaporates more quickly than water at room temper 9t6e 1 ,)ims+z2cguvd lv1jhjature. What can you infer about the molecular prop) 6mj u19v+hgs21ijze vl,tcderties of one relative to the other?

Explain why a hot humid day is far more uncomfor3 -lw pgjjk8i .wvncn;yo t27j0i,t5u1g lie0table than a hot dry day at the same temperat yii 1e0gop72-,kl8 tgu.w3ln5 i0 jcvtwjn j;ure.

Is it possible to boil water at room temi8sltbpb,) a )perature (20 $^{\circ} $ C) without heating it? Explain.

Consider two days when the air temperature is the sameo5 oh9 pxlz1,e but the humidity is different. Which is more dense, the dry air or thez ,lp1ho5x oe9 humid air at the same T? Explain.

Explain why it is dangerous to opetis ,w20xjyse5pr jy 73y5kf-n the radiator cap of an overheated automobile engy0pwy3x js5kf27e-yj, s5i trine.

Why does exhaled air appear as a little white cloud in the wd;sr(dsl v,)x inter (Fig. 13–28)?

  How many atoms are there in a 3.4-gramwh3rf7 pvc4l 4n9un4i copper penny?   $ \times10^{22}$ atoms of Cu

  How does the number of atoms in a 26.5-gram gold rin)usgz3 )l5ucz v4 bs9. )mwlgcg compare to the number in a silver ring of the )slwbm5)3 z v)u49zc.gug cslsame mass?$N_{Au}$ =    $N_{Ag}$

  “Room temperature” is often taken to be 68°F. What is this on the Ceh1gd*zd;o hs 0lsius scale? hd0h g;zods1*   $^{\circ} $ C
(b) The temperature of the filament in a lightbulb is about 1800 $^{\circ} $ C. What is this on the Fahrenheit scale?    $^{\circ} $ F

  Among the highest andy1 xn(*vva yc.o9+z8ssuguy 4 lowest temperatures recorded are 136 $^{\circ} $F in the Libyan desert and -129 $^{\circ} $F in Antarctica. What are these temperatures on the Celsius scale?high =    $^{\circ} $ C
low =    $^{\circ} $ C

  (a) 15 $^{\circ} $ below zero on the Celsius scale is what Fahrenheit temperature?    $^{\circ} $ F
(b) 15 $^{\circ} $ below zero on the Fahrenheit scale is what Celsius temperature?   $^{\circ} $ C

  In an alcohol-in-glass thermometer, the alcod*i:r( o w1+ 6bmm7/p2 / wwsrjuvbukdhol column has length 11.82 cm at 0.06wb ou2w /md( r*j/wp:7bi 1dsrkumv+ $^{\circ} $ C and length 22.85 cm at 100.0 $^{\circ} $ C. What is the temperature if the column has length
(a) 16.70 cm,    $^{\circ} $ C
(b) 20.50 cm?    $^{\circ} $ C

  A concrete highway is built of slabs upcn )7t 8dz24z0mpyn12 m long (20 $^{\circ} $ C). How wide should the expansion cracks between the slabs be (at 20 $^{\circ} $ C) to prevent buckling if the range of temperature is -30 $^{\circ} $ C to +50 $^{\circ} $ C?    m

  Super Inva$^{TM}$, an alloy of iron and nickel, is a strong material with a very low coefficient of linear expansion [0.2$ \times10^{ -6}$(C?)$^{-1}$]
A 2.0-m-long tabletop made of this alloy is used for sensitive laser measurements where extremely high tolerances are required. How much will this table expand along its length if the temperature increases 5.0 $^{\circ} $ C? Compare to tabletops made of steel.   $ \times10^{-6 }$ m    $ \times10^{-4 }$ m

  The Eiffel Tower (Fig. 13–29) is built of wrought iron approximately 300 m tm5na68- je whfe0qy+k all. Estimate how much its height changes b85 k0j-+ewnhe6mqyfa etween July (average temperature of 25°C) and January (average temperature of 2 $^{\circ} $ C). Ignore the angles of the iron beams, and treat the tower as a vertical beam.    m

  To make a secure fit, rivets that are larger tham+ c+ ;wk1xpyzn the rivet hole are often used and the rivet is cooled (usually in dry ice) before it is placed in the hole. A steel rivet 1.871 cm in diameter is to be placed in a hole 1.869 c km1;c+yz+pxwm in diameter at 20 $^{\circ} $ C. To what temperature must the rivet be cooled if it is to fit in the hole?    $^{\circ} $ C

  The density of water ath: 1,a6cx4p upavc6.e3i fqsy 4 $^{\circ} $ C is $ 1\times10^{3 }kg/m^3$ What is water’s density at 94 $^{\circ} $ C?    kg/$m^3$

  A quartz sphere is 8.7 ywn )5gjx* p-byhzafu(:d1li,*cf /p5 cm in diameter. What will be its change in volume if it is heated frf nzpipyh da*-(u 5b1g*,wfyj /x:)lcom 30 $^{\circ} $ C to 200 $^{\circ} $ C?    $ \times10^{ -2}cm^3$

  An ordinary glass is f1cny5 or9 wl sg5.5unbi6ia r9illed to the brim with 350.0 mL of water at 100.0$^{\circ} $ C. If the temperature decreased to 20.0 $^{\circ} $ C, how much water could be added to the glass?    mL

  It is observed that 55.50 mL of water ntc5;o9.r ,.qgycm l bat 20 $^{\circ} $ C completely fills a container to the brim. When the container and the water are heated to 60 $^{\circ} $ C, 0.35 g of water is lost. (a) What is the coefficient of volume expansion of the container?    $ \times10^{-5 }$ /$C^0$(b) What is the most likely material of the container? The density of water at 60°C is 0.98324g/ml.

  (a) A brass plug is to be placed in a ri4a a (fu+e(c+ucoxh2w ng made of iron. At 20 $^{\circ} $ C, the diameter of the plug is 8.753 cm and that of the inside of the ring is 8.743 cm. They must both be brought to what common temperature in order to fit?    $^{\circ} $ C
(b) What if the plug were iron and the ring brass?    $^{\circ} $ C

If a fluid is contain -5.. mrsplqefao7oq :ed in a long, narrow vessel so it can expand in essentially one direction only, show that the effrs.pmq lq5f.a- : o7eoective coefficient of linear expansion is approximately equal to the coefficient of volume expansion $\beta$.

(a) Show that the change in thei 7rv:g ,)qf4lh vg0ujlzadbww0*22e density $\rho$ of a substance, when the temperature changes by $\Delta$T is given by $\rho$ = -$\beta$$\rho$$\Delta$T
(b) What is the fractional change in density of a lead sphere whose temperature decreases from 25 $^{\circ} $ C to -40 $^{\circ} $ C？

A uniform rectangular plate of length l and widt(wra7yw 3ugv 2h w has coefficient of linear expansion yuwr2ag wv(7 3$\alpha$ Show that, if we neglect very small quantities, the change in area of the plate due to a temperature change $\Delta$T is $\Delta$A = 2$\alpha l w$$\Delta$T See Fig. 13–30.

Show that for an isotropic soygt7s b :c4d6vlid, $\beta$ = 3$\alpha$ if the amount of expansion is small. $\beta$ and $\alpha$ are the coefficients of volume and linear expansion, respectively. [Hint: Consider a cubical solid, and neglect very small quantities. See also Problem 18 and Fig. 13–30.]

  The pendulum in a grandfather clock is maipz,e 4k: 8h*w 7zpxdede of brass and keeps perfect time at 1:8,p ke*4whx ze7zidp7 $^{\circ} $ C. How much time is gained or lost in a year if the clock is kept at 25 $^{\circ} $ C? (Assume the frequency dependence on length for a simple pendulum applies.)$\approx$    min(Round to the nearest integer)

  (a) The tube of a mercury thermo* akanc12xbk-4d : ipj(y uf:bmeter has an inside diameter of 0.140 mm. The bulkn*-k ac(fy::a4xbj i2b1pudb has a volume of 0.255 $cm^3$ How far will the thread of mercury move when the temperature changes from 11.5 $^{\circ} $ C to 33.0 $^{\circ} $ C? Take into account expansion of the Pyrex glass.    cm(b) Determine a formula for the length of the mercury column in terms of relevant variables. Ignore tube volume compared to bulb volume.

  A 23.4-kg solid alum/l22k4 q u88hxz ydgniinum cylindrical wheel of radius 0.41 m is rotating about its axle on frlx/yzn848 ugdq i 2hk2ictionless bearings with angular velocity $\omega$ = 32.8 rad/s If its temperature is now raised from 20.0 $^{\circ} $ C to 75.0 $^{\circ} $ C, what is the fractional change in $\omega$?   

  An aluminum bar has the desired length when at 15°C. Howupz - o2n /yjsl0boq*1 much stress is required to keep it at this length if the temperature increases t 0ypu o1l/zb 2-*sqnojo 35 $^{\circ} $ C?    $ \times10^{7 }$ N/$m^2$

(a) A horizontal steel I-beam of cross-sectiotegbp2m7 j8pd238p 9v:jf jhs nal area 0.041$m^2$ is rigidly connected to two vertical steel girders. If the beam was installed when the temperature was 30$^{\circ} $ C, what stress is developed in the beam when the temperature drops to -30 $^{\circ} $ C (b) Is the ultimate strength of the steel exceeded? (c) What stress is developed if the beam is concrete and has a cross-sectional area of 0.13$m^2$ Will it fracture?

  A barrel of diameter 134.122 /t9(0siiph- t(hoi wzio9ju1 cm at 20$^{\circ} $ C is to be enclosed by an iron band. The circular band has an inside diameter of 134.110 cm at 20$^{\circ} $ C. It is 7.4 cm wide and 0.65 cm thick.
(a) To what temperature must the band be heated so that it will fit over the barrel? $\approx$   $^{\circ} $ C(Round to the nearest integer)
(b) What will be the tension in the band when it cools to 20$^{\circ} $ C?    N

  What are the following temperatures on the Kelvin scalioq4;((z j feke:
(a) 86$^{\circ} $ C,    K
(b) 78$^{\circ} $F,    K
(c) -100$^{\circ} $C    K
(d) 5500°C,    K
(e) -459$^{\circ} $F    K

  Absolute zero is what temperhh3yc 5(8eoi uature on the Fahrenheit scale?    $^{\circ} $ F

  Typical temperatures in the interior of the Earth and Sun a hknl2ty)* (c7b k+iidre about 4000$^{\circ} $ C and $ \times10^{6 }$ $^{\circ} $ C respectively.
(a) What are these temperatures in kelvins?    K    $ \times10^{ 6}$K
(b) What percent error is made in each case if a person forgets to change $^{\circ} $ C to K? $\approx$    %(Round to the nearest integer) $\approx$    %(Round to three decimal places)

  If 3 $m^2$ of a gas initially at STP is placed under a pressure of 3.20 atm, the temperature of the gas rises to 38.0$^{\circ} $ C. What is the volume?    $m^3$

  In an internal combustion engine, air at atmospheric pressure andirge 9jc+:r 5y a temperature ofy:e+cjig r9 r5 about 20$^{\circ} $C is compressed in the cylinder by a piston to $\frac{1}{9}$ of its original volume (compression ratio = 9.0). Estimate the temperature of the compressed air, assuming the pressure reaches 40 atm.    $^{\circ} $ C

  Calculate the density of oxygen at STP using the ideal gas l4 tk qkv*ju,-fcx a1h*aw.    kg/$m^3$

  A storage tank contains 21.6 kg of nitrogen (/ x gdi0 y*iif-b9sljk(3i3bo$N_2$) at an absolute pressure of 3.65 atm. What will the pressure be if the nitrogen is replaced by an equal mass of $CO_2$    atm

  A storage tank at STP sz0vcf6+f1q. fgu 8ajcontains 18.5 kg of nitrogen ($N_2$)
(a) What is the volume of the tank? $\approx$   $m^3$(“Round to one decimal places)
(b) What is the pressure if an additional 15.0 kg of nitrogen is added without changing the temperature?    $ \times10^{5 }$Pa    atm

  If 18.75 mol of helium gas is at x l6ufblk-w6 g 7l fc-jl 8x80,5hyyej10.0$^{\circ} $C and a gauge pressure of 0.350 atm, (a) calculate the volume of the helium gas under these conditions.    $m^3$
(b) Calculate the temperature if the gas is compressed to precisely half the volume at a gauge pressure of 1.00 atm.    $^{\circ} $ C

  What is the pressure inside a 35.0-L container hoxpo)x 6i:9gd olding 105.0 kg of argon gas at 385 x:gi6) o9d opxK?   $ \times10^{ 8}$Pa

  A tank contains 26.0 kg qzcj+od.ou 2v.wx9z. of $O_2$ gas at a gauge pressure of 8.70 atm. If the oxygen is replaced by helium, how many kilograms of the latter will be needed to produce a gauge pressure of 7.00 atm?    kg He

  A hot-air balloon achieves ic iolrjn;,aff4;n4wq)*v-k v; ws h: its buoyant lift by heating the air inside the balloon, which makes it less dense than the air outside. va q h;;4ckw,vijnr4fifo ): w*l;s n-Suppose the volume of a balloon is 1800 $m^3$ and the required lift is 2700 N (rough estimate of the weight of the equipment and passenger). Calculate the temperature of the air inside the balloon which will produce the required lift. Assume that the outside air temperature is 0 $^{\circ} $ C and that air is an ideal gas under these conditions. What factors limit the maximum altitude attainable by this method for a given load? (Neglect variables like wind.) $\approx$    $^{\circ} $ C(Round to the nearest integer)

  A tire is filled with air a 92sra bw3 /b t).7jbhfzkg;rdt 15 $^{\circ} $ C to a gauge pressure of 220 kPa. If the tire reaches a temperature of 38 $^{\circ} $ C, what fraction of the original air must be removed if the original pressure of 220 kPa is to be maintained?    %

  If 61.5 L of oxygen at 180a0nb grto*v *.0 $^{\circ} $ C and an absolute pressure of 2.45 atm are compressed to 48.8 L and at the same time the temperature is raised to 50.0°C, what will the new pressure be?    atm

  A helium-filled balloon escapes a +vz0 y*fh1cf+skjic s( v-yy;child’s hand at sea level and 20.0 $^{\circ} $ C. When it reaches an altitude of 3000 m, where the temperature is 5.0 $^{\circ} $ C and the pressure is only 0.70 atm, how will its volume compare to that at sea level?    times the original volume

  Calculate the number of molecgi(f:j/4n;xkq huc r5s0q s e(ules / $m^3$ in an ideal gas at STP.    $ \times10^{25 }$ molecules /$m^3$

  How many moles of water are t(dc2 8)xolsw mc/(42kiu :lgqyjk +n x5nugn 5here in 1.000 L? How many molecules?    mol    $ \times10^{25 }$ molecules

  Estimate the number of (-- rix+7 mbqdga) moles,    $ \times10^{22 }$ moles and (b) molecules of water in all the Earth’s oceans. Assume water covers 75% of the Earth to an average depth of 3 km. $\approx$    $ \times10^{46 }$ molecules

  A cubic box of volumtp5 vr.pk ,:lre 5.1$ \times10^{ -2}m^3$ is filled with air at atmospheric pressure at 20 $^{\circ} $ C. The box is closed and heated to 180 $^{\circ} $ C. What is the net force on each side of the box?    N

  Estimate how many molecules of air are in each 2.0-L breath you inhale tha rst2-+p l)cqq z21iut57h cmyt were2s)c t2qyqiprmuz17- lc+h5t also in the last breath Galileo took. [Hint: Assume the atmosphere is about 10 km high and of constant density.]   $\frac{molecules}{breath}$

  (a) What is the average translational kinetic energy of an oxygen molen914bdu wr bu;cule at STP bu9u rwdb14;n?    $ \times10^{-21 }$ J
(b) What is the total translational kinetic energy of 2.0 mol of $O_2$ molecules at 20 $^{\circ} $ C?   $ \times10^{3 }$ J

  Calculate the rms speed of helium atoms near the surfr-/s/b uv7(8pjkcvro ace of the Sun at a temperature of about 6000 K /jurb pv(7sck8-/ovr .    m/s

  By what factor will th7 gd nsr6 32yyv7p/bmge rms speed of gas molecules increase if the temperature is incgys3vg/ 7db ypr6n2 m7reased from 0 $^{\circ} $ C to 100 $^{\circ} $ C?   

  A gas is at 20 $^{\circ} $ C. To what temperature must it be raised to double the rms speed of its molecules?    $^{\circ} $ C

  Twelve molecules have te,6x ur r hqougu1b(4yqdn+(.he following speeds, given in units of km/s: 6, 2, 4, 6, 0, 4, 1, 8, 5, 3, 7, and 861,er (y(n x rdgqu+b q.u4ouh. Calculate the rms speed. $v_{rms}$ =    km/s

  The rms speed of molecules in a gas at 20.0 llr9d/ ft,n6ti ,yh; y$^{\circ} $ C is to be increased by 1.0%. To what temperature must it be raised?    $^{\circ} $ C

  If the pressure of a gas is doubled while its volume is held cons(jps;eu)qtl)0 y 2y wktant, by what factor does;ptk (2eslj q0uy)w) y $v_{rms}$ change?   

Show that the rms speed of sf :j+1ei/p cxmolecules in a gas is given by $v_{rms}$ = $\sqrt{3P\\rho}$ where P is the pressure in the gas, and $\rho$ is the gas density.

Show that for a mixture of two gases at the same temper)s macyu m/09p ter+z:ature, the ratio of their rms speeds is equal to th p/mz:aytcsmr+)9e0u e inverse ratio of the square roots of their molecular masses.

  What is the rms speed of nitrogen molecules contained in an c bh:n wp6.pq.)j)zx fnu+zt;8.5$-m^3$ volume at 2.1 atm if the total amount of nitrogen is 1300 mol?    m/s

  Calculate (a) the rms speed of an oxygen molecule at 0 m+f; 3aew:ltkz1nkhf(jw h4q7av ,v 2v y* *zi$^{\circ} $ C    m/s
(b) determine how many times per second it would move back and forth across a 7.0-m-long room on the average, assuming it made very few collisions with other molecules.    round trips per sec

  What is the average distance between nitrogen molecules xic*u1kjdz+-at STP?    $ \times10^{-9 }$m

  (a) Estimate the rms speed of an amino acid whcfi/l, hxf91 l,3d:l3iqdlfx ose molecular mass is 89 u in a liviiix 9llxql 3h dc/,l,df:ff13 ng cell at 37 $^{\circ} $ C.    m/s
(b) What would be the rms speed of a protein of molecular mass 50,000 u at 37 $^{\circ} $ C?    m/s

Show that the pressure P of a gas can be writtwwhy+x1w 6 *ppu7/izren P = $\frac(1)(3)\rho v^2$ where $\rho$ is the density of the gas and v is the rms speed of the molecules.

  The two isotopes of uranium,xq7rdlj;c- h d+op ;1y $^{235}$U and $^{238}$U (the superscripts refer to their atomic mass), can be separated by a gas-diffusion process by combining them with fluorine to make the gaseous compound UF$_6$ Calculate the ratio of the rms speeds of these molecules for the two isotopes, at constant T.   

(a) At atmospheric pressure, in what phasjs5s64lw ejhj-4nb -h es can $CO_2$ exist? (b) For what range of pressures and temperatures can $CO_2$ be a liquid? Refer to Fig. 13–21.

Water is in which phase when the pressure is 0.01 atm and the t e1q+f ti)-7itk3 *ij.flgkro emperature is (a)f kg7j+ .q) -1ifek3litirto* 90 $^{\circ} $ C, (b) -20 $^{\circ} $ C.

  What is the dew point (approximately) if the humidity is 50% on a dac b9d 1oje*;f*tpmwg 2y when the temperaturp *m *g1;ftoed2jw9 bce is 25 $^{\circ} $ C?$\approx$    $^{\circ} $ C(Round to the nearest integer)

  What is the air pressure at a place where wxcp3mu /r24ps id 3o0 lkjnd8hpor6 08ater boils at 90 $^{\circ} $ C?    torr    Pa    atm

  If the air pressure at a particular place in the mountains is 0.7np9p,3r*p,a jfzp 7,qr1duba2 atm, estimate the trz,uapb 7d9*p jf,13qa,nrppemperature at which water boils. $\approx$ =    $^{\circ} $ C

  What is the temperature on a day when the partial pres9/cnogj z6c3yu3uw ( psure of water is 530 Pa and the rwuc6pz/ yj(no3gu 9c3elative humidity is 40%? $\approx$ =    $^{\circ} $ C(Round to the nearest integer)

  What is the partial pressure of waterhxee;sbif9;,p6wf+i on a day when the temperature is 25 $^{\circ} $ C and the relative humidity is 35%?    Pa

  What is the approximate pressure inside a pressure cooker if the wa1 v,y poicb,t.ter is boiling at a temperatu yv,obpc1it ,.re of 120 $^{\circ} $ C? Assume no air escaped during the heating process, which started at 20 $^{\circ} $ C.    atm

  If the humidity in a room of 1 0s z1aaj/tbm0bmf+a volume 680$m^3$ at 25 $^{\circ} $ C is 80%, what mass of water can still evaporate from an open pan?    kg

  Air that is at its dew point o3t6ncg/s3 fdz(lthg/bw8fs: f 5 $^{\circ} $ C is drawn into a building where it is heated to 25. What will be the relative humidity at this temperature? Assume constant pressure of 1.0 atm. Take into account the expansion of the air.    %

  Estimate the time needed for a gsy:qn9z3 yac 4lycine molecule (see Table 13–4) to diffuse a dis3:z sc49yqya ntance of 15 $\mu m$ in water at 20$^{\circ} $ C if its concentration varies over that distance from 1 mol/$m^3$ to 0.4 mol/$m^3$ Compare this “speed” to its rms (thermal) speed. The molecular mass of glycine is about 75 u. t $\approx$    s ([color=rgba(0, 0, 0, 0.85)]Round to one decimal places) $v_{diffuse}$    $ \times10^{ -5}$ m/s
$v_{rms}$    m/s

  Oxygen diffuses from the surface of insectsqaz2h *fwogm9cs4(w24dku1c2sd e.zv, *vjg to the interior through tiny tubes called tracheae. An average trachea is about 2 mm long and has cross-secte 1 k2g ,4az zqg94 2mohjfvcvds.*duww(2s*cional area of $ 2\times10^{-9 } m^2$ Assuming the concentration of oxygen inside is half what it is outside in the atmosphere,
(a) show that the concentration of oxygen in the air (assume 21% is oxygen) at 20$^{\circ} $ C is about 8.7 mol/$m^3$ then $\approx$    mol/$m^3$(Round to one decimal places)
(b) calculate the diffusion rate J,    $ \times10^{-11 }$ mol/s
(c) estimate the average time for a molecule to diffuse in. Assume the diffusion constant is $ 1\times10^{-5 } m^2/s$    s

  A precise steel tape measure has been calibratedv7;vc/0 re1; ovsk;jp ivu; 3lb h;ogz at 20$^{\circ} $C. At 34$^{\circ} $C,
(a) will it read high or low,
(b) what will be the percentage error?    $ \times10^{-4 }$ %

  A precise steel tape measure has been calib+ih0e q m-(ladrated at 20$^{\circ} $C. At 34$^{\circ} $C,
(a) will it read high or low,
(b) what will be the percentage error?    $ \times10^{-4 }$ %

  A Pyrex measuring cup waslt+(4e x1shal calibrated at normal room temperature. How much error will be made in a recipe calling for 300 mL of cool water, if the water and the cup are s+exh lt1l4 (ahot, at 80$^{\circ} $C, instead of at 20$^{\circ} $C? Neglect the glass expansion.$\approx$    ml

  The gauge pressure in a helium gas cylinder is initiac:y;e aq4 ro8:yw)) iq+ej n6 l0fhmvdlly 28 atm. After many balloons have been blown up, the gauge pressureely6inha0;:mc yrevqd:o8)q4 f) j+w has decreased to 5 atm. What fraction of the original gas remains in the cylinder?   

  Estimate the number of air molecules in a room of leng.abb04 kezy ;c f,y,)m)ja nulth 6.5 m, width 3.1 m, and height 2.5 m. Assume the temperla,c4ua.b ,0e fy jmnb zyk;))ature is 22$^{\circ} $C. How many moles does that correspond to?    $\times10^{27 }$ molecules    moles

  In outer space the density of matter is about one atom p1ih9uocs/u n3 u fh8r*er $cm^3$ mainly hydrogen atoms, and the temperature is about 2.7 K. Calculate the rms speed of these hydrogen atoms, and the pressure (in atmospheres).$v_{rms}$ =    m/s    $ \times10^{-22 }$ atm

  The lowest pressure attainable using the best availafmhy p 4e3,qg1 xu/u5lble vacuum techniques is aboufp1u,x4qme3/lhyu5g t $10^{-12} N/m^2$ At such a pressure, how many molecules are there per $cm^3$ at 0$^{\circ} $C?    $\frac{molecules}{cm^3}$

  If a scuba diver filllr, mh3,sbug) n g(qgi szj 29ik.e7a4s his lungs to full capacity of 5.5 L when 10 m below the surface, to what volume w,i3 j2gg49r)k( aisng lz q7eush,.mbould his lungs expand if he quickly rose to the surface? Is this advisable?    L

  A space vehicle returning from the Moon enters Earth’s atmos1 o*c0 n 6rkiu7r6ujnkphere at a speed of about 40,000 k7uu kki 0r6cn n*6j1orm/h Molecules (assume nitrogen) striking the nose of the vehicle with this speed correspond to what temperature? (Because of this high temperature, the nose of a space vehicle must be made of special materials; indeed, part of it does vaporize, and this is seen as a bright blaze upon reentry.)    K

  The temperature of an ideal gas is v2 p31sdwn qd1za3a (dincreased from 110$^{\circ} $C to 360$^{\circ} $C while the volume and the number of moles stay constant. By what factor does the pressure change? By what factor does $v_{rms}$ change?$\frac{P_2}{P_1}$ =    $\frac{(v_{rms})_2}{(v_{rms})_1}$ =   

  A house has a volume ofa,,y slplq-+8igo l7q 770m$^2$ (a) What is the total mass of air inside the house at 20$^{\circ} $C?    kg
(b) If the temperature drops to -10$^{\circ} $C what mass of air enters or leaves the house?    kg

  From the known value of atmospheric pres5e fi) *jql*s;r0 oqfpsure at the surface of the Earth, estimate the total number of air molel0e r* oif)qpjf; qs5*cules in the Earth’s atmosphere.    $ \times10^{44 }$ molecules

  What is the rms speed of nitrogen molecules co4cvw0u+0o ya; hadt,u+b+b 6*uaun) vdev* zr ntained in a 7.6$-m^3$ volume at 4.2 atm if the total amount of nitrogen is 1800 mol?    m/s

  A standard cylinder of ,v1+ou d) q3let ld-x esd14ni0c9tai oxygen used in a hospital has gauge pressure = 2000 psi (13,800 kPq +) cx1eiui,9 staed -tn14d0 vldlo3a) and at T = 259K How long will the cylinder last if the flow rate, measured at atmospheric pressure, is constant at 2.4 L/min. $\approx$    hour

  An iron cube floats in a bowl of liquid mercury at03dh euuo(2*huyi+fe 0$^{\circ} $C. (a) If the temperature is raised to 25$^{\circ} $C, will the cube float higher or lower in the mercury? ----待选择----lowerheigher 
(b) By what percent will the fraction of volume submerged change?    %

  The density of gasoline1kkebg*b(7 cfqi3 p,e at 0$^{\circ} $C is 0.68$ \times10^{3 }kg/m^3$ What is the density on a hot day, when the temperature is 38$^{\circ} $C?    kg/$m^3$
What is the percentage change?    %

  If a steel band were to fit snugly aro 09c)yx*hhz9*h uo gkxund the Earth’s equator at 25$^{\circ} $C, but then was heated to 45$^{\circ} $C, how high above the Earth would the band be (assume equal everywhere)?    m

  A brass lid screws tightly onto a glass jar atp6moves j1;* 4m1 negskx / 8:x2ifsp.wr-fer 20$^{\circ} $C. To help open the jar, it can be placed into a bath of hot water. After this treatment, the temperatures of the lid and the jar are both 60$^{\circ} $C. The inside diameter of the lid is 8.0 cm at 20$^{\circ} $C. Find the size of the gap (difference in radius) that develops by this procedure.    cm

  The first length standard, adoptedui8ce s.jd r)d q2*uf5 in the 18$^{th}$ century, was a platinum bar with two very fine marks separated by what was defined to be exactly 1 m. If this standard bar was to be accurate to within $\pm1.0 \mu m$ how carefully would the trustees have needed to control the temperature? The coefficient of linear expansion for platinum is $ 9\times10^{ -6}C/^{-1}$. $\pm$ =    C$^{\circ} $

  A scuba tank, when fully charged, has a pressure of 195 atm,rh4y qho 9 d5hn4p(ok at 20$^{\circ} $C. The volume of the tank is 11.3 L.
(a) What would the volume of the air be at 1.00 atm and at the same temperature?    L
(b) Before entering the water, a person consumes 2.0 L of air in each breath, and breathes 12 times a minute. At this rate, how long would the tank last?    min
(c) At a depth of 20.0 m of sea water and temperature of 10$^{\circ} $C, how long would the same tank last assuming the breathing rate does not change?    min

  The escape speed fro1kb)ffk5bv( v1fkx n;m the Earth is $ 1.12\times10^{4 } m/s$ so a gas molecule travelling away from Earth near the outer boundary of the Earth’s atmosphere would, at this speed, be able to escape from the Earth’s gravitational field. At what temperature is the average speed of
(a) oxygen molecules,    $ \times10^{5 }$K
(b) helium atoms equal to $ 1.12\times10^{4 } m/s$    $ \times10^{4}$K
(c) Can you see why our atmosphere contains oxygen but not helium?

  A 1.0-kg trash-can lidx0p hng9 6ywia3c.x; red:x8.s mo,jk is suspended against gravity by tennis balls thrown vertically upward at it. How many tennis balls per second must rebound from the lid elastically, assuming they have a mass of 0.060 kg and 0krcx6ed.hx9;wosg:3xmn yi. p, j8 aare thrown at 12m/s   balls/s

  A scuba diver releases a 3.00-cm-diameter (spherical) bubble of air from a depthwsi3mmb+ wv;w ai:8(q of 14.0 m in a lake. Assume the temperature is constant at 298 K, and the air behaves as a perfect gasaw( msiv+w8w3qi; b:m. How large is the bubble when it reaches the surface?    cm

  Calculate the total water vapor pressure 5/bexqxq k8d/ )u(pe6 nz awjekmu*99in the air on the following two days: 6mkq z9xeued 5)u/ w9b /xjpka8n*q (e
(a) a hot summer day, with the temperature 30$^{\circ} $C and the relative humidity at 40%;    Pa
(b) a cold winter day, with the temperature 5$^{\circ} $C and the relative humidity at 80%.    Pa

  A sauna has 7$m^3$ of air volume, and the temperature is 90$^{\circ} $C. The air is perfectly dry. How much water (in kg) should be evaporated if we want to increase the relative humidity from 0% to 10%? (See Table 13–3.)    kg

  Estimate the percent difference in the density of iron at Swsmbaw +gkkt,4r .0(dTP, and when it is a sob gw+ , mkt(.4srwdk0alid deep in the Earth where the temperature is 2000$^{\circ} $C and under 5000 atm of pressure. Assume the bulk modulus (90$\times 10^9N/m^2$) and the coefficient of volume expansion do not vary with temperature and are the same as at STP.    %  ----待选择----decreaseincrease 

(a) Use the ideal gas law to show +( c ufvdu owa80b6hw1that, for an ideal gas at constant pressure, the coefficient of volume expansion is edb av+wfc1 w6(o8 hu0uqual to $\beta$ = 1/T where T is the temperature in kelvins. Compare to Table 13–1 for gases at T = 293K (b) Show that the bulk modulus (Section 9–5) for an ideal gas held at constant temperature is B = P where P is the pressure.

  In humid climates, people constantly dehumidify their f( zre) zlr/n+w1o vtrnn72o4cellars to prevent rot and mildew. If the rtr4orn/(+e wzv)onn1zf7 l 2cellar in a house (kept at 20$^{\circ} $C) has 95 $m^2$ of floor space and a ceiling height of 2.8 m, what is the mass of water that must be removed from it to drop the humidity from 95% to a more reasonable 30%?    kg